Precise measurements of basal melting have been made at a series of 14 sites lying within a few kilometres of the grounding line of the Ronne Ice Shelf, Antarctica, where the ice thickness ranges from 1570 to 1940 m. The study was conducted over the course of 1 year and included a detailed survey of the horizontal deformation, as well as phase-sensitive radar measurements of the vertical displacement of both internal reflecting horizons and the ice-shelf base. Results from the surface survey show that the long-term viscous strain rate is modulated at tidal frequencies by (probably) elastic strains of order 10−5 per metre of tidal elevation. The radar measurements show a similar modulation of the long-term thinning/thickening of the ice shelf, with thickness oscillations up to a few centimetres in range. The long-term trends in ice thickness determined at points moving with the ice-shelf flow are consistent with a steady-state thickness profile. Vertical strain rates within the ice shelf were determined from the relative motion of internal reflectors. At two sites the observations were sufficient to discern the effect of tidal bending about a neutral surface 60% of the way down the ice column. Coincident measurements of horizontal and vertical strain imply a Poisson's ratio of 0.5, and this combined with the asymmetric bending gives rise to the observed oscillations in thickness. At a number of sites the long-term viscous strain rates were found to be a linear function of depth. For an ice shelf this is an unexpected result. It can be attributed to the presence of significant vertical shear stresses set up close to the grounding line where the ice is still adjusting to flotation. Additional vertical motion arising from firn compaction was observed within the upper layers of the ice shelf. The additional motion was consistent with the assumption that firn density is a function only of the time since burial by steady surface accumulation. With both spatial and temporal fluctuations in the vertical strain rate accurately quantified it was possible to estimate the vertical motion of the ice-shelf base in response. Differences between the calculated and observed motion of the basal reflector arise because of basal melting. Derived melt rates at the 14 sites ranged from −0.11 ± 0.31 to 2.51 ± 0.10 ma−1, with a mean of 0.85 m a−1 and a standard deviation of 0.69 m a−1, and showed no signs of significant sub-annual temporal variability. There was no obvious global correlation with either ice thickness or distance from the grounding line, although melt rates tended to decrease downstream along each of the flowlines studied. Previous estimates of basal melting in this region have been obtained indirectly from an assumption that the ice shelf is locally in equilibrium and have included a broad range of values. Only those at the lower end of the published range are consistent with the directly measured melt rates reported here.